Epi

Mekkora az behatolási mélység egy fémes felületen és mekkora az epiréteg határán az amplitúdó.

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Mx:

\(div E = 0\)

\(div B = 0\)

\(rot E = -\dot B\)

\(rot B = \mu_0 J +\frac{1}{c^2}\dot E\)

kint: \((z<0)\) \(j=0\)

bent: \((z>0)\) \(j=\sigma E\)

\(z<0\)

\(E(z, t) = (E_i, 0, 0)\cdot e^{i(k_i z - \omega t)}+(E_r, 0, 0) \cdot e^{-i(k_r z + \omega t)}\)

\(B(z, t) = (0, B_i, 0)\cdot e^{i(k_i z - \omega t)}+(0, B_r, 0) \cdot e^{-i(k_r z + \omega t)}\)

\(rot E = \left( \begin{array}{c} \partial_y E_z -\partial_z E_y \\ \partial_z E_x - \partial_x E_z \\ \partial_y E_x - \partial_x E_y \end{array} \right) = (0, E_i i k_i \cdot e^{i(k_i z - \omega t)}, 0)-(0, E_r i k_r \cdot e^{i(k_r z + \omega t)}, 0)\)

\(rot B = (B_i i k_i \cdot e^{i(k_i z - \omega t)}, 0, 0)-(B_r i k_r \cdot e^{i(k_r z + \omega t)}, 0, 0)\)

Maxwellbe visszaírva:

\(E_i i k_i = i \omega B_i\)

\(E_r i k_r = i \omega B_r\)

\(-i k_i B_i = \frac{1}{c^2} (-i \omega E_i)\)

\(k_i B_i = \frac{\omega}{c^2} E_i\)

\(k_r B_r = \frac{\omega}{c^2} E_r\)

\(k^2_{i/r} = \frac{\omega}{c^2}\)